In the first scenario, we let \(\epsilon \sim N(0, 0.2^2(1 + 2(X - ^{*T})^2))\) , which is referred to as Heteroskedastic Gaussian scenario later on.
We compare the proposed smoothed decorrelated score test (SDS) with the decorrelated score test method (DS) [1]} and Honest confidence region method (Honest) [2]} from the “hdm” package.
We fix the significance level at \(0.05\)  and firstly evaluate the performance of the tests under the null hypothesis \(H_0: \beta ^*_1 = 0\) . In this case, we set \(\beta ^*_1 = 0\) .
Note that the R code for the DS and Honest approaches is tailored for the high-dimensional logistic regression, which differs from the above data generating process.
